The Experts below are selected from a list of 150 Experts worldwide ranked by ideXlab platform

John Suckling - One of the best experts on this subject based on the ideXlab platform.

Tiago Simas - One of the best experts on this subject based on the ideXlab platform.

  • commentary semi Metric Topology of the human connectome sensitivity and specificity to autism and major depressive disorder
    Frontiers in Neuroscience, 2016
    Co-Authors: Tiago Simas, John Suckling
    Abstract:

    This study was funded by the UK Medial Research Council (grants: G0802226 and G0701919), the National Institute for Health Research (NIHR) (grant: 06/05/01) and the Behavioural and Clinical Neuroscience Institute (BCNI), University of Cambridge. The BCNI is jointly funded by the Medical Research Council and the Wellcome Trust. Additional support was received from the NIHR Cambridge Biomedical Research Centre. CCH is supported by a Parke Davis Fellowship from the University of Cambridge and resides at Columbia University.

  • semi Metric Topology of the human connectome sensitivity and specificity to autism and major depressive disorder
    PLOS ONE, 2015
    Co-Authors: Tiago Simas, Shayanti Chattopadhyay, Cindy C Hagan, Prantik Kundu, Ameera X Patel, Rosemary Holt, Dorothea L Floris, Julia Graham
    Abstract:

    Introduction The human functional connectome is a graphical representation, consisting of nodes connected by edges, of the inter-relationships of blood oxygenation-level dependent (BOLD) time-series measured by MRI from regions encompassing the cerebral cortices and, often, the cerebellum. Semi-Metric analysis of the weighted, undirected connectome distinguishes an edge as either direct (Metric), such that there is no alternative path that is accumulatively stronger, or indirect (semi-Metric), where one or more alternative paths exist that have greater strength than the direct edge. The sensitivity and specificity of this method of analysis is illustrated by two case-control analyses with independent, matched groups of adolescents with autism spectrum conditions (ASC) and major depressive disorder (MDD).

Julia Graham - One of the best experts on this subject based on the ideXlab platform.

  • semi Metric Topology of the human connectome sensitivity and specificity to autism and major depressive disorder
    PLOS ONE, 2015
    Co-Authors: Tiago Simas, Shayanti Chattopadhyay, Cindy C Hagan, Prantik Kundu, Ameera X Patel, Rosemary Holt, Dorothea L Floris, Julia Graham
    Abstract:

    Introduction The human functional connectome is a graphical representation, consisting of nodes connected by edges, of the inter-relationships of blood oxygenation-level dependent (BOLD) time-series measured by MRI from regions encompassing the cerebral cortices and, often, the cerebellum. Semi-Metric analysis of the weighted, undirected connectome distinguishes an edge as either direct (Metric), such that there is no alternative path that is accumulatively stronger, or indirect (semi-Metric), where one or more alternative paths exist that have greater strength than the direct edge. The sensitivity and specificity of this method of analysis is illustrated by two case-control analyses with independent, matched groups of adolescents with autism spectrum conditions (ASC) and major depressive disorder (MDD).

Katsuro Sakai - One of the best experts on this subject based on the ideXlab platform.

  • subdivisions of simplicial complexes preserving the Metric Topology
    Canadian Mathematical Bulletin, 2012
    Co-Authors: Kotaro Mine, Katsuro Sakai
    Abstract:

    Let be the Metric polyhedron of a simplicial complex . In this paper, we characterize a simplicial subdivision of preserving the Metric Topology for as the one such that the set of vertices of is discrete in . We also prove that two such subdivisions of have such a common subdivision.

  • small subdivisions of simplicial complexes with the Metric Topology
    Journal of The Mathematical Society of Japan, 2011
    Co-Authors: Katsuro Sakai
    Abstract:

    D. W. Henderson established the Metric Topology vertion of J. H. C. Whitehead's Theorem on small subdivisions of simplicial complexes. However, his proof is valid only for locally finite-dimensional simplicial complexes. In this note, we give a complete proof of Henderson's Theorem for arbitrary simplicial complexes.

  • Hausdorff hyperspaces of $R^m$ and their dense subspaces
    Journal of the Mathematical Society of Japan, 2008
    Co-Authors: Wieslaw Kubis, Katsuro Sakai
    Abstract:

    Let $CLB_H(X)$ denote the hyperspace of closed bounded subsets of a Metric space $X$, endowed with the Hausdorff Metric Topology. We prove, among others, that natural dense subspaces of $CLB_H(R^m)$ of all nowhere dense closed sets, of all perfect sets, of all Cantor sets and of all Lebesgue measure zero sets are homeomorphic to the Hilbert space $\ell_2$. Moreover, we investigate the hyperspace $CL_H(R)$ of all nonempty closed subsets of the real line $R$ with the Hausdorff (infinite-valued) Metric. We show that a nonseparable component of $CL_H(R)$ is homeomorphic to the Hilbert space $\ell_2(2^{\aleph_0})$ as long as it does not contain any of the sets $R, [0,\infty), (-\infty,0]$.

  • the spaces of closed convex sets in euclidean spaces with the fell Topology
    Bulletin of The Polish Academy of Sciences Mathematics, 2007
    Co-Authors: Katsuro Sakai, Zhongqiang Yang
    Abstract:

    Let ConvF (R) be the space of all non-empty closed convex sets in Euclidean space R endowed with the Fell Topology. In this paper, we prove that ConvF (R) ≈ R × Q for every n > 1 whereas ConvF (R) ≈ R× I. Let Conv(X) be the set of all non-empty closed convex sets in a normed linear space X = (X, ‖·‖). We can consider various topologies on Conv(X). In the paper [6], the AR-property of the spaces Conv(X) with the Hausdorff Metric Topology, the Attouch-Wets Topology, and the Wijsman Topology has been studied. In this paper, we shall consider the Fell Topology on Conv(X), which is generated by the sets of the form U− = {A ∈ Conv(X) | A ∩ U 6= ∅} and (X \K)+ = {A ∈ Conv(X) | A ⊂ X \K}, where U is open and K is compact in X. This Topology is also defined on the set Conv∗(X) = Conv(X) ∪ {∅}. By ConvF (X) and ConvF (X), we denote the spaces Conv∗(X) and Conv(X) admitting the Fell Topology. In case X is finite-dimensional (equivalently locally compact), ConvF (X) is a locally compact metrizable space and ConvF (X) is its Alexandorff onepoint compactification. It is easy to see that ConvF ((0, 1)) is homeomorphic to (≈) the triangle with two vertices removed, ∆ \ {(0, 0), (1, 1)}, where ∆ = {(x, y) ∈ I | x 6 y} ⊂ I. Since ConvF (R) ≈ ConvF ((0, 1)), we have ConvF (R) ≈ ∆ \ {(0, 0), (1, 1)} ≈ R× I, hence it follows that ConvF (R) ≈ ∆/{(0, 0), (1, 1)} ≈ (S × I)/({pt} × I), 1991 Mathematics Subject Classification. 54B20, 54D05, 54E45, 57N20.

Cindy C Hagan - One of the best experts on this subject based on the ideXlab platform.

  • semi Metric Topology of the human connectome sensitivity and specificity to autism and major depressive disorder
    PLOS ONE, 2015
    Co-Authors: Tiago Simas, Shayanti Chattopadhyay, Cindy C Hagan, Prantik Kundu, Ameera X Patel, Rosemary Holt, Dorothea L Floris, Julia Graham
    Abstract:

    Introduction The human functional connectome is a graphical representation, consisting of nodes connected by edges, of the inter-relationships of blood oxygenation-level dependent (BOLD) time-series measured by MRI from regions encompassing the cerebral cortices and, often, the cerebellum. Semi-Metric analysis of the weighted, undirected connectome distinguishes an edge as either direct (Metric), such that there is no alternative path that is accumulatively stronger, or indirect (semi-Metric), where one or more alternative paths exist that have greater strength than the direct edge. The sensitivity and specificity of this method of analysis is illustrated by two case-control analyses with independent, matched groups of adolescents with autism spectrum conditions (ASC) and major depressive disorder (MDD).